U.S. patent application number 13/680318 was filed with the patent office on 2013-05-23 for computed-tomography system and method for determining volume information for a body.
The applicant listed for this patent is Jan Boese, Yu Deuerling-Zheng, Sabine Heiland, Martin Wagner. Invention is credited to Jan Boese, Yu Deuerling-Zheng, Sabine Heiland, Martin Wagner.
Application Number | 20130129172 13/680318 |
Document ID | / |
Family ID | 48221878 |
Filed Date | 2013-05-23 |
United States Patent
Application |
20130129172 |
Kind Code |
A1 |
Boese; Jan ; et al. |
May 23, 2013 |
COMPUTED-TOMOGRAPHY SYSTEM AND METHOD FOR DETERMINING VOLUME
INFORMATION FOR A BODY
Abstract
A tomogram of a body is provided. Projection-image data obtained
by a radiation-based projection method is used for providing the
tomogram. Initial voxel data are first specified for a plurality of
voxels of the body. Synthetic projection-image data are generated
based upon a projection rule modeling a course of the projection
method. Projection-error data is determined by comparing the
synthetic projection-image data with the real projection-image
data. The projection-error data are imaged on the basis of a
back-projection rule dependent on the projection rule so that
voxel-error data are produced. Correction data is generated from
the voxel-error data by a gradient-based optimizing algorithm,
wherein corrected voxel data are generated using the correction
data.
Inventors: |
Boese; Jan; (Eckental,
DE) ; Deuerling-Zheng; Yu; (Forchheim, DE) ;
Heiland; Sabine; (Heidelberg, DE) ; Wagner;
Martin; (Heidelberg, DE) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Boese; Jan
Deuerling-Zheng; Yu
Heiland; Sabine
Wagner; Martin |
Eckental
Forchheim
Heidelberg
Heidelberg |
|
DE
DE
DE
DE |
|
|
Family ID: |
48221878 |
Appl. No.: |
13/680318 |
Filed: |
November 19, 2012 |
Current U.S.
Class: |
382/131 |
Current CPC
Class: |
G06T 7/0012 20130101;
G06T 11/003 20130101 |
Class at
Publication: |
382/131 |
International
Class: |
G06T 7/00 20060101
G06T007/00 |
Foreign Application Data
Date |
Code |
Application Number |
Nov 22, 2011 |
DE |
102011086771.6 |
Claims
1. A method of determining volume information of a body, wherein
projection-image data are available which were produced by a
radiation-based projection method, the method of determining volume
information comprising: specifying initial voxel data for a
plurality of voxels of the body, generating synthetic
projection-image data based upon the initial voxel data with a
projection rule modeling a course of the radiation-based projection
method, comparing the synthetic projection-image data with the real
projection-image data and determining projection-error data,
imaging the projection-error data on the basis of a back-projection
rule dependent on the projection rule and generating voxel-error
data, determining correction data from the voxel-error data by a
gradient-based optimizing algorithm, and determining corrected
voxel data based upon the correction data.
2. The method as claimed in claim 1, wherein a mathematical model
for describing a time dependency of the voxel data is defined for
at least one voxel of the body, wherein the model includes at least
one model parameter and wherein the correction data include update
vector data for the at least one model parameter.
3. The method as claimed in claim 2, wherein the model indicates a
mathematical dependency of a contract-medium concentration on a
time parameter and includes a gamma-variate function.
4. The method as claimed in claim 1, wherein projection-image data
are available for two projection images recorded under different
measuring conditions, wherein projection-image data of a first
projection image are subtracted as a baseline from projection-image
data of a second projection image or wherein, from the
projection-image data of the first projection image, a constant
offset value is determined for a mathematical model which is used
to model the projection-image data of the second projection
image.
5. The method as claimed in claim 1, wherein the optimizing
algorithm is based on the Levenberg-Marquardt method.
6. The method as claimed in claim 1, wherein the initial voxel data
are determined based upon a filtered back projection of the real
projection-image data.
7. The method as claimed in claim 1, wherein a sequence of
method-specific steps is performed repeatedly, wherein previously
determined corrected voxel data are used as initial voxel data in a
repeated step, and wherein a degree of error dependent on the
projection-error data is iteratively reduced.
8. The method as claimed in claim 7, wherein a first value for a
step size of the gradient-based optimizing algorithm is set for a
predefined number of repetitions of the sequence of method-related
steps and a second value that is greater than the first is set for
succeeding repetitions.
9. The method as claimed in claim 7, wherein, after the
method-specific steps are performed at least once, the obtained
corrected voxel data are used as initial voxel data for which
voxel-error data are again determined, wherein only a subset of the
voxel-error data is selected for computing further correction data
according to a predefined criterion.
10. The method as claimed in claim 1, wherein a product formed from
the voxel-error data and from a Jacobi matrix is stored in a memory
of a data-processing device which performs the method.
11. The method as claimed in claim 1, wherein the correction data
are computed from the voxel-error data numerically on the basis of
a Cholesky factorization.
12. The method as claimed in claim 1, wherein the voxel data for at
least two voxels is computed simultaneously with two different
processors.
13. The method as claimed in claim 1, wherein the corrected voxel
data are determined for projection-image of a computed tomography
or positron-emission tomography.
14. A computed-tomography system, comprising: a data-processing
device, and an x-ray detector coupled to the data-processing
device, wherein the data-processing device is configured to execute
a method of determining volume information of a body as claimed in
claim 1.
15. A non-transitory computer readable medium storing instructions
which, when executed on a computer, perform a method of determining
volume information of a body as claimed in claim 1.
Description
CROSS REFERENCE TO RELATED APPLICATIONS
[0001] This application claims priority of German Patent
Application No. 10 2011 086 771.6 DE filed Nov. 22, 2011. All of
the applications are incorporated by reference herein in their
entirety.
FIELD OF INVENTION
[0002] A method for determining volume information for a body is
provided, wherein projection-image data are used which were
produced by a radiation-based projection method. Further, a
computed-tomography system is provided.
BACKGROUND OF INVENTION
[0003] Image information about a body's internal structure may be
determined non-invasively by radiation-based projection methods,
for example computed tomography. The body may be the body of a
patient, for example, whether human or animal. An inanimate object
such as, for instance, a sample of material or a machine, may also
be understood here as a body.
[0004] To be able to mutually differentiate the body's individual
constituents, differences in said constituents are used in regard
of their absorption characteristics in terms of the radiation with
which the body is irradiated within the scope of the projection
method. The body is therein thought of as being divided into what
are termed voxels, which are small volume elements. For each of
said voxels the absorption characteristic of the material located
therein is then determined based on the projection-image data. The
totality of such "attenuation values" for the individual voxels is
here referred to as voxel data.
[0005] The voxel data are obtained by irradiating the body with the
radiation from different directions and registering a projection
image for each of said irradiating operations on a projection
surface by means of, for example, electronic pixel sensors. Said
projection images then each constitute a shadow of the body's
individual elements. The projection-image data is nowadays usually
assembled into a two-dimensional tomogram by means of what is
termed filtered back projecting so that inferences may be made from
the plurality of projection images about the nature of the body's
materials in the individual voxels, i.e. the voxel data.
[0006] Filtered back projecting requires that the characteristics
of the body's individual volume elements do not to change while the
projection images are being recorded, often in succession, which
means that the voxel data are independent of time. Hence, with that
method it is not possible, for example, to show functionally, which
is to say dynamically, how a contrast medium spreads along a
patient's blood vessels. There being just a single projection image
for each perfusion state of the contrast medium in the body,
artifacts may appear during reconstructing of a tomographic image
due to the temporal change in the voxel data.
[0007] An alternative approach to back projecting is offered using
an algebraic reconstruction technique (ART). With that method it is
possible to take account of there only ever being one projection
image for a specific perfusion state of a contrast medium. An
example of an ART algorithm of such kind is the method described in
the work published by Neukirchen et al. (C. Neukirchen, M.
Giordano, and S. Wiesner, "An Iterative Method for Tomographic
X-ray Perfusion Estimation in a Decomposition Model-Based
Approach": Medical Physics, vol. 37, no. 12, pp. 6125-6141,
December 2010). It is a method whereby the time-dependency of the
voxel data representing the blood vessels in a patient's body is
determined on the basis of a principal component analysis (PCA).
The PCA is here used for determining basic functions for the course
of the voxel values over time so that the time-dependent
attenuation value in each voxel can then be described by
superimposing said basic functions.
SUMMARY OF INVENTION
[0008] An object is to provide a tomogram of a body, which tomogram
is as free as possible from artifacts. The object is achieved by a
method and a computed-tomography system as claimed in the
independent claims. Advantageous developments of the method are
described in the dependent claims
[0009] The method processes projection-image data obtained by a
radiation-based projection method, for example computed tomography.
Volume information is obtained about individual voxels of the body,
which is information about the material of the body in the
individual voxels in terms of an interaction between said material
and the radiation employed.
[0010] At a first step, initial voxel data are specified for a
plurality of voxels of the body. Said data may be values that are
independent of the real measurement, for example zeroes, or a mean
value computed from the projection-image data.
[0011] Synthetic projection-image data are then generated from the
initial voxel data. The projection rule employed is, for instance,
a projection matrix, models the course of the projection method via
which the real projection-image data was obtained. For each real
projection image, a corresponding, synthetic projection image
recorded from the same beam direction as the real projection image
will thus be produced from the initial voxel data.
[0012] At another step of the method, the synthetic
projection-image data are compared with the real projection-image
data. The determined differences form projection-error data serving
as a measure of the extent to which the initial voxel data diverges
from the body's real voxel data requiring being determined.
[0013] According to the method, said projection-error data, which
has been determined for the individual projection images, is
combined into voxel-error data on the basis of a back-projection
rule. Said back-projection rule constitutes a reversal of the
projection rule that was mentioned, although it does not have to be
a distinct reversal.
[0014] Once the voxel-error data relating to the individual voxels
is available, correction data for the individual voxels is
determined at another step of the method by a gradient-based
optimizing algorithm. Corrected voxel data describing the real
situation prevailing in the body better than the initial voxel data
is determined on the basis of said correction data.
[0015] The method has the advantage that tomograms may be produced
which have significantly fewer image artifacts than, for example,
tomograms produced by filtered back projecting.
[0016] The method also allows a time dependency of the voxel data
to be taken into account so that functional representations, such
as are necessary, for example, for visualizing a perfusion of a
contrast medium in a living body, will also be possible. Account
may likewise be taken of breathing movements or other local
displacements of individual elements of the body. For that purpose,
a development of the method provides a mathematical model for
describing a time dependency of the voxel data to be defined for at
least one voxel of the body. Said model includes at least one model
parameter. Update vector data forming correction data by means of
which the at least one model parameter is updated may then be
determined for a parameterized model of such kind on the basis of
the gradient-based optimizing algorithm.
[0017] An embodiment allows the cited visualizing of perfusion
processes and for that purpose provides for the model to indicate a
mathematical time-dependency of a contract-medium concentration.
The mathematical model may be formed on the basis of a
gamma-variate function or gamma distribution.
[0018] Particularly high-contrast representations may be provided
if projection images recorded under at least two different
measuring conditions are available. A possible example is firstly
to record the projection images before a contrast medium is
injected and then to repeat the recording during the injection
process. Once projection images produced under different measuring
conditions are available, then according to a development of the
method, projection-image data of one of the projection images will
be subtracted as what is termed a baseline from the other
projection image's projection-image data or a constant offset value
will be determined there from for the described mathematical model.
Temporal changes will then be rendered particularly prominent
thereby.
[0019] The method may be realized on the basis of different
gradient-based optimizing algorithms. Examples include the Newton
method and Gauss-Newton method. The Levenberg-Marquardt method is
suitable in connection with projection-image data relating to human
or animal bodies for obtaining tomograms having few artifacts. Said
method may be implemented efficiently in terms of memory.
[0020] As already described, very easily determined initial values
may be used as initial voxel data. It is also possible to receive
voxel data starting with zero values. Use of filtered
back-projecting in providing initial voxel data has proved
surprisingly expedient. The method, which is to be counted among
the ART methods, may in other words be combined with filtered
back-projecting when the initial voxel data is being provided.
Thus, blood-vessel and tissue voxels may during initializing first
be coarsely segmented using a conventional reconstructing method
(such as filtered back-projecting just cited). In each case, a mean
vessel or, as the case may be, tissue curve describing the temporal
curve of the intensity values may then be computed for the
initializing process.
[0021] The method is designed for iteratively improving the voxel
data. The sequence of method-specific steps is for that purpose
performed repeatedly. For each repetition the respectively
previously determined corrected voxel data are specified as the
initial voxel data. A degree of error that is dependent on the
projection-error data is thus iteratively reducible, meaning that
the voxel data will describe to an ever greater extent the
situation prevailing in the body.
[0022] What the gradient-based optimizing algorithm therein does is
as a function of the projection-error data to in each case
determine correction values for the individual items of voxel data
themselves or for model parameters by means of which the improved
voxel data are then computed using a model. The correction values
are in the simplest case added to the current values (voxel values
or model-parameter values). What the magnitude of said correction
values may be is, in the case of a gradient-based optimizing
algorithm, as a rule determined by what is termed a step size of
the algorithm. It is therein customary to start with a large step
size and to reduce it as the number of repetitions or iterations
increases when the algorithm starts converging. What, though, has
proved particularly expedient in connection with the method is a
development wherein a first, relatively small value is initially
set for a step size of the gradient-based optimizing algorithm for
a predefined number of repetitions of the sequence of
method-related steps. A second value that is greater than the first
is not set until afterwards for succeeding repetitions. A
particularly good convergence characteristic of the optimizing
algorithm may be achieved in that way in connection with
projection-image data.
[0023] All voxel-error data is as a rule fed to the gradient-based
optimizing algorithm to allow all available error information to be
included in determining the correction data. Ever smaller values
for the correction data will therein be obtained with the
optimizing algorithm approaching a (local or global) error minimum
as the sequence of method-related steps is repeated. Iterative
computing of the voxel data may be immediately followed by a
correction phase of the method to prevent the algorithm from
therein aiming only for a local optimum leaving an error in the
voxel data unable to be corrected by means of the optimizing
algorithm. In said correction phase, voxel-error data are first in
the manner already described again determined from initial voxel
data which may be, for example, corrected voxel data from a
previous iteration. Instead, though, of then using all said
voxel-error data for computing further correction data, an analysis
of the voxel-error data is first performed in the correction phase.
Only a subset of the voxel-error data is therein determined for an
ensuing computation of further correction data. All voxel-error
data meeting a predefined criterion is selected for that purpose.
The set of voxel-error data having negative values is therein a
particularly suitable subset. The correction data are then at a
succeeding step computed only on the basis of said subset, which in
trials resulted in improved voxel data.
[0024] The method may also be implemented very efficiently in terms
of memory. Thus a development of the method provides for storing
not the voxel-error data itself but a product formed from the
voxel-error data and from a Jacobi matrix in a memory belonging to
the data-processing device by which the method is performed. A
Jacobi matrix of such kind is as a rule a constituent of a
gradient-based optimizing algorithm. When the correction data is
being computed, as a rule only said product is required that is
formed from the Jacobi matrix and voxel-error data and produces a
result vector requiring significantly less memory space than the
vector of the voxel-error data itself.
[0025] The memory requirements may be reduced even further by
computing the correction data from the voxel-error data numerically
on the basis of a Cholesky factorization. Said computing may be
implemented as what is termed an in-place calculation
(data-substituting calculation).
[0026] Voxel-data computing may be accelerated in the case of
projection-image data about which it is known that it represents
images of a body that was not significantly moved during the
recording process. It will then be possible to compute voxel data
simultaneously for different voxels on two different processor
cores because the voxel data for a specific voxel does not have to
be taken into account for computing another voxel's voxel data. The
voxel data will then be mutually independent.
[0027] Computed tomography, especially C-arm computed tomography,
and positron-emission tomography have proved particularly suitable
as radiation-based projection methods for obtaining the
projection-image data.
[0028] In this connection, another aspect relates to a
computed-tomography system, in particular a C-arm
computed-tomography system, in which an x-ray detector is coupled
to a data-processing device, for example a personal computer, which
is equipped for implementing an embodiment of the method.
BRIEF DESCRIPTION OF THE DRAWINGS
[0029] FIG. 1 is a flowchart relating to an embodiment of the
method and
[0030] FIG. 2 is a diagram illustrating a correction phase of an
embodiment of the method.
DETAILED DESCRIPTION OF INVENTION
[0031] FIG. 1 is a flowchart relating to a method 10 for computing
time-dependent voxel data V(t) from predefined real
projection-image data rP(t). Real projection-image data rP(t) may
have been obtained by, for example, a C-arm CAT scanner 12. An
x-ray source 14 of a C-arm CAT scanner 12 may have been rotated
along with an x-ray detector 16 around a human patient's body 18.
The intensity values--registered by x-ray detector 16--of
individual pixels of a sensor of x-ray detector 16 are combined in
a numeric vector forming real projection-image data rP(t). A
sequence of sectional images 18', that will be displayed on a
screen 22, of CAT scanner 12 is then computed for the patient's
body 18 by a data-processing device 20 of CAT scanner 12.
[0032] Real projection-image data rP(t) may have been obtained, for
example, in a recording cycle of eight seconds (8 sec) during which
a C-arm was swiveled through an angular range of 200.degree. to
210.degree. with projection images being obtained having a uniform
angular spacing. The patient may have been injected with a contrast
medium during the recording process. The sequence of sectional
images 18' will then visualize the perfusion of the contrast medium
in the vessels of body 18. The method may be used also for
projection-image data that has been recorded in a longer recording
cycle, for example forty seconds (40 sec). A projection-image
database produced over such a long period of time could not be used
in the case of a conventional method for computing voxel data.
[0033] Voxel data V(t) for sectional image 18' is iteratively
improved by the method 10. At an initializing step S10, a vector is
specified having initial voxel data V0(t) and forming at a first
iteration step n=0 the vector for voxel data V(t) which means
V(t)=V0(t). The initial vector V0(t) is computed on the basis of a
dynamic model for the representation of the time-dependent volume
data based on a mathematical model describing the dynamic process
of concentration variance in the contrast medium in individual
volume elements of the body. For that purpose it is possible to
use, for example, a gamma-variate function y(t) that includes four
model parameters A, B, C, and D:
y(t)=A*(t-D).sup.B*e.sup.-(t-D)*C for (t-D)>0
and
y(t)=0 for (t-D).ltoreq.0.
[0034] The values corresponding to the individual recording
instants of real projection data rP(t) may be used for time
parameter t. The values for model parameters A through D are
changed by the method in the manner described below in such a way
that on the basis of gamma-variate function y(t) it will be
possible using the values obtained for parameters A through D for
the individual recording instants to compute voxel data V(t)
enabling a sequence of realistic sectional images 18' to be
computed. For that purpose, proceeding from the initial vector data
V(t)=V0(t), synthetic projection-image data P(t) is first computed
in the following manner using a projection matrix Q(t):
FP: P(t)=Q(t)*V(t).
[0035] Projection matrix Q(t) constitutes a projection rule (FP:
forward projection) by which the course of recording the real
projection-image data rP(t) may be modeled. Each line of projection
matrix Q(t) contains weightings for each voxel V(t). The weighting
depends on how much of the voxel was irradiated by the x-ray beam
at instant t in the respective rotational position of x-ray source
14 and x-ray detector 16. If it is assumed that all of body 18 was
in the field of view (FOV) of x-ray source 14 and x-ray detector 16
for a projection image, then the sum of each column of projection
matrix Q(t) will be one.
[0036] Synthetic projection-image data P(t) is at a step S14
compared with real projection-image data rP(t). One possibility for
performing said comparison is to compute projection-error data R(t)
as the difference between the projection images' intensity
values:
R(t)=rP(t)-P(t).
[0037] Other error computations are possible such as forming the
square of the difference.
[0038] At an ensuing step S16, a voxel error E(t) is computed for
voxel data V(t) as forming the basis of current iteration n.
Projection-error data R(t) is for that purpose computed into an
error volume by way of a back-projection rule (BP: back
projection). The back-projection rule derives from projection
matrix Q(t) as transposed matrix Q.sup.T(t):
BP: E(t)=Q.sup.T(t)*R(t).
[0039] For each individual voxel i and for the individual recording
instants, an estimation is given in voxel-error data E(t) of error
Fi(t) existing between volume data V(t) as produced from the
current values of model parameters A through D and true,
inaccessible voxel data Vi(t) of individual voxels i:
Fi(t)=Vi(t)-y(t).apprxeq.Ei(t),
wherein Ei(t) stands for the values from voxel-error data E(t) that
belong to a voxel i.
[0040] For said error Fi(t), an update vector K containing four
correction values, each of which is added to one of model
parameters A to D, is computed for each voxel i at a step S18 in an
optimization phase S18' (OPT: optimization phase) on the basis of a
gradient-based optimizing method, for example the
Levenberg-Marquardt method. Combining the values--valid for
iteration n--of model parameters A to D of a voxel i into a
parameter vector G(n) will produce the values for ensuing iteration
n+1 as follows:
G(n+1)=G(n)+K.
[0041] Update vector K is computed by solving the following
equation provided by the Levenberg-Marquardt method:
OPT: (J.sup.T*J+L*I)*K=J.sup.T*Ei(t),
wherein J is the Jacobi matrix for estimation error Fi(t) in terms
of the four model parameters A to D, matrix I forms the unit
matrix, and L indicates the gradation of the gradient-based
optimizing algorithm.
[0042] Solving said equation for K allows the values for model
parameters A to D to be computed as parameter vector G(n+1) and
then new voxel data V(t) to be computed for the individual instants
at which the projection images were determined.
[0043] Be it assumed for the example shown in FIG. 1 that sequence
of steps S12 to S18 is executed a total of eight times. Be it
further assumed that optimizing algorithm will afterwards have
converged to such an extent for there only to be marginal changes
in value at step S18 not resulting in any appreciable improvements
to voxel data V(t). In order nonetheless to achieve a further
improvement, the optimization phase S18' is changed over to a
correction phase S18'' (CORR: correction phase). The decision
whether to execute a correction or optimization step for a specific
voxel depends on the magnitude of the values of last update vector
K and can be different for each voxel. It is possible to switch
between optimization and correction at any time.
[0044] Correction phase S18'' is explained in more detail below
with the aid of FIG. 2. Shown in FIG. 2 for an individual voxel i
is voxel data V(t, i) for the individual instants of the 8 sec
recording period. Voxel data V(t, i) has here been converted into
intensity values, what are termed Houndsfield units HU. What
results from gamma-variate function y(t) at the end of the eighth
iteration, n=8, is curve 24. Shown for comparison is a true curve
26 as would have to be obtained in the case of an ideal estimation.
The correction phase produces (from curve 24) a curve 28 that
deviates less from ideal curve 26. Also shown in FIG. 2 is
volume-error data Ei(t) plotted in the form of crosses. In order to
correct curve 24, in iteration n=9, in the example all values to
which Ei(t)<0 applies, are selected for each voxel i from
voxel-error data E(t), meaning from Ei(t). The other values of
Ei(t) are set to zero. A new update vector K is then computed on
the basis of those values only.
[0045] Real projection data rP(t) may also include projection-image
data for what is termed a mask run consisting of a measuring cycle
with no injection of contrast medium. The projection-image data
obtained there from may be subtracted from the projection-image
data produced during contrast-medium injecting in order to improve
the contrast in sectional images 18'. The projection-image data of
the mask run can also be used as the basis for a constant offset
value y0 for gamma-variate function y(t), for which in this case
what applies to (t-D)>0 is:
y(t)=y0+A*(t-D).sup.B*e.sup.-(t-D)*C.
[0046] Iteratively optimizing each voxel value in a volume is very
compute-intensive. Parallel computing may help to shorten the
algorithm's convergence time. The nature of the method described
here renders it capable of a high degree of parallelizing and
enables it to be executed in a graphics processor, for instance, by
processor cores operating simultaneously in parallel. Thus each
voxel may be treated in a separate thread. To drastically reduce
the memory requirements, it may be provided to store not the Jacobi
matrix J itself but only the product J.sup.T*J, from which a
4.times.4 matrix is produced. Voxel-error data Ei(t) may equally be
stored exclusively in the form J.sup.T*Ei(t). Finally, the equation
system for computing update vector K may be computed on the basis
of a Cholesky decomposition and a forwards-backwards substitution,
as a result of which there will be an in-place calculation, which
is to say a memory-neutral calculation.
[0047] The step size L is initially kept artificially small for the
first iterations and only increased as the number of iterations
increases.
[0048] The example shows how an iterative 4-dimensional ART method
for reconstructing volume information for a body is possible even
if a computed-tomography system's C-arm may not be rotated fast
enough to provide a sufficient number of projection images for
temporal processes at every instant. Each voxel's dynamics are here
modeled by a gamma-variate function. The parameters for the model
are estimated by an optimizing algorithm based on the
Levenberg-Marquardt method.
[0049] Reconstructing the parameters of the gamma-variate function
enables the perfusion and blood flow in the body to be computed.
Using a gamma-variate function as a dynamic model means that only
the very few values for the model parameters themselves will have
to be computed, which makes this method significantly more robust
than estimating the entire course of the values on the basis of a
PCA. The risk of over-fitting will also be reduced. The method
offers extensive scope for parallelizing and may also be executed
on graphics processors.
[0050] While specific embodiments have been described in detail,
those with ordinary skill in the art will appreciate that various
modifications and alternative to those details could be developed
in light of the overall teachings of the disclosure. For example,
elements described in association with different embodiments may be
combined. Accordingly, the particular arrangements disclosed are
meant to be illustrative only and should not be construed as
limiting the scope of the claims or disclosure, which are to be
given the full breadth of the appended claims, and any and all
equivalents thereof. It should be noted that the term "comprising"
does not exclude other elements or steps and the use of articles
"a" or "an" does not exclude a plurality.
* * * * *